In this study, the effect of various microcapsule sizes on the mechanical properties of microcapsule-based polymeric materials was investigated using the finite element method and validated with experimental outcomes. Specimens containing 5wt. % of microcapsules were fabricated to calculate the elastic modulus, and maximum tensile stress, and to validate numerical results. To consider the error, five tests were performed for all samples, and results were reported on average. The average errors between the numerical outcomes and experimental results were 4.74% and 5.35% for maximum tensile stress and elastic modulus, respectively. The coaxial electrospraying method was used for synthesizing microcapsules made of alginate (shell) and epoxy (core). A scanning electron microscope (SEM) was used to calculate the diameter of the capsules. To develop an empirical model for the average microcapsule diameter (AMD) and carry out the optimization process, response surface methodology (RSM) with central composite design was used. Also, analysis of variance was employed to validate the accuracy of the model. The effects of three parameters, including voltage, needle size, and the distance between the tip of the needle to the collector, on average microcapsule diameter, were investigated. The empirical model was validated by a confirmation run, and the determined error (1.93%) between the predicted and experimental results indicates the precision of the model. The numerical study indicated that microcapsule-based self-healing polymers containing smaller microcapsules tolerate higher stresses. However, the effect of the microcapsules’ size on the elastic modulus of a representative volume element was negligible.
This work deals with the wave propagation analysis in functionally graded carbon nanotubes (CNTs)-reinforced composite beams lying on an elastic medium. Despite the large amount of experimental and theoretical studies in the literature on the mechanical behavior of composite structures strengthened with CNTs, limited attention has been paid to the effect of an axial graduation of the reinforcing phase on the mechanical response of CNTs-reinforced composite beams. In this paper, CNT fibers are graded across the beam length, according to a power-law function, which expresses a general variation from a linear to parabolic pattern. An Euler-Bernoulli beam theory is considered herein to model the CNTs-reinforced composite structure resting on a Winkler–Pasternak foundation, whose governing equations are derived from the Hamiltonian principle. The theoretical solution of the problem checks for the sensitivity of the mechanical response to different parameters, i.e., the wave number, power index, Winkler and Pasternak coefficients, that could serve for further computational/experimental studies on the same problem, even from a design standpoint.
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